Cycling Forces

We have seen that cycles are inertial. In the absence of any pushing or pulling, they do one of two things. At rest, they stay at rest. When in motion, they continue in motion, moving in a straight line at the same velocity. In Mechanics, inertial behavior is described using Newton’s First Law.  Motion is where things get interesting, but at least on the flat, we see something approximating inertial motion. If you stop pedaling, you will coast for a good distance before aerodynamics first and finally rolling resistance bring you to a stop.

With motion, we move into the realm of Newton’s Second Law which modified for cycling says a cycle will continue to move inertially unless there are forces pushing and pulling on it. So when cycling, what are the forces we need to take into account?


You can see we actually only have seven forces we need to understand, though cycle efficiency is not a push-pull , rather a property of the cycle itself. We can group these into several categories: forward, resistive, and gravitational. We will get into more detail about each of these, but for the moment, we are simply looking to understand at a high level what they are.

  • Cyclist generated forces
    • Pedal force
    • Forward force
  • Resistive forces
    • Rolling road resistance
    • Aerodynamic drag
    • Bicycle mechanical resistance
  • Gravitational forces

Forward forces:

The forward forces on are generated from within the cyclist-cycle system. It is the cyclist that is propelling both forward. The Cyclist is pushing on the pedals and moving them around in a circle. The process is dynamic in that the force on either pedal varies throughout a cycle. However, we can also approximate this by an average pedal force per cycle. But if your feet are moving around in a circle, how can they be moving you forward as well? In fact, if your feet are moving at a rate of 4-5 mph, how is it you can easily get a bike on the flats up to 20 mph?

The answer is your bicycle is a machine designed to translate pedal motion into forward motion that is applied by the rear wheel to the road. It is a process that begins at the pedals, is transmitted to the rear wheel through the chain, and ultimately through the rear wheel to the road. Notice that the front wheel is simply along for the ride. Bicycles are rear-wheel drive vehicles.

The three forward force elements are therefore intimately connected with each other. The Pedal Force is a true push and measurable by many of the available power devices. The Cycle Efficiency is a measure of how the pedaling motion is transmitted to the rear wheel. Think about when you shift gears to say climb a hill. When you downshift and maintain your current cadence, you move slower. This is a number that you effectively set as you ride. Each possible gear combination has a number describing the gear ratios of the two discs connecting the pedals and the rear wheel.

Finally, the chain is what turns the rear wheel and completes the process of transmitting pedal force to the rear wheel. This is where the “rubber meets the road.”

Resistive Forces:

These are exactly what they sound like. They are the forces that the cyclist must overcome to keep the cycle moving forward. They include three resistance types: Rolling, Aerodynamic, and Bicycle.

Rolling Resistance: If you have taken a Physics class, you have already encountered resistance. Normally you are introduced to two types of resistance: Standing and Sliding. If you imagine a block sitting on a surface with a string that can be used to pull it, standing resistance measures how hard you need to pull to get the block moving, and sliding resistance how hard you need to pull to keep it moving. As it turns out, it takes more force to start an object sliding than it does to keep it sliding. If anyone has watched any of the Ninja shows, you have seen a visual demonstration of this.

When you consider cycling, you add a third type of resistance called Rolling Resistance. Tires do not slide across a surface, rather that roll. Consequently, rolling resistance is significantly smaller than sliding resistance. Considering you are operating on a surface of dry concrete, how do these three coefficients compare? The standing resistance coefficient is 1.0, the sliding coefficient is 0.800, and the rolling resistance is 0.002. This makes it 400 times easier to roll across the surface rather than slide.

In most cases, rolling resistance has minimal impact. The one important case is when you are rolling to a stop. If you start out at say 20 mph, aerodynamic drag will be predominant, but once you slow to 10 mph, rolling resistance becomes comparable and ultimately is what brings you to a stop.

Aerodynamic Drag: When cycling, you are doing so within a dynamic fluid called air. And in doing so as with any fluid, there is an inherent drag you must deal with. It is also a velocity-dependent resistance, that is, the faster you try to move, the more aerodynamic drag you have to deal with. At higher and racing speeds, drag is your fundamental limiting factor and one of the primary reasons cyclists go to extreme measurements to minimize drag. Here is an example from Tour de France races in the Eighties. Cycling shoes had laces resulting in a rough interface to the air. To smooth that out and reduce drag over the hours long rides, the cyclist would tape over the laces to present a smoother interface.

At a high level, we simply need to understand that aerodynamic drag is fundamental to cycling and that its magnitude is directly dependent on the speed at which you are moving. Imagine you are a parachutist. As you jump out of a plane, you are initially dropping slowly though picking up speed rapidly. The aerodynamic drag therefore starts from near zero and rapidly picks up until you reach a point it is large enough that the net force of your weight is equal to the amount of drag pushing up on you. From Newton’s Second Law, the net force at that point is zero and you stop picking up speed. You have reached what is called terminal velocity.

Bicycle Resistance: Bicycles are mechanical. They chains and gears and pedals, and the process of riding, some of the energy is dissipated as heat. This results in some loss of efficiency in transferring energy from your pedals to the rear wheel. Fortunately, bicycles are highly efficient and this loss is of the order of 5%.

Gravitational Forces:

We treat gravitational forces as its own category because it is a rather versatile component to bike riding. It is always a factor, but it varies depending on how you are riding. If you are riding on the flats, you are neither ascending nor descending. However, rolling resistance is a function of the combined weight of the cyclist-cycle. Then if you are ascending, you know how difficult it can quickly become depending on the hill slope. Gravity is seeking to pull you back down the hill. On ascents, gravity is not your friend. Then if you are descending, gravity becomes your new best friend. It seeks to pull you forward down the hill, so much so, you may not even need to pedal.

Cycling Force Summary:

Cycling forces are easy to understand, but we have clearly only looked at what they are from a high level. But that is all we need to create a force model for what is happening when we are cycling. This model will provide us with a qualitative overview of the cycling process, but not a quantitative one from which we can perform calculations. That is something we will get to eventually, but not before we have a picture of how all these pieces fit together.


Cycling as seen through the eyes of elite cyclists.